-24. Non-stabilities of mixed type Euler-Lagrange k-cubic-quartic functional equation in various normed spaces

John Michael Rassias; Mohan Arunkumar; Elumalai Sathya

Volume 1, Issue 1 , February 2019, , Pages 1-43

http://dx.doi.org/10.30495/maca.2019.679849

Abstract
  In this paper, we introduce and examine the generalized Ulam-Hyers stability of fixed Euler-Lagrange  k-Cubic-Quartic functional Equationf(x+ky) + f(kx+y) + f(x-ky) + f(y-kx) = k2[2f(x+y) + f(x-y) + f(y-x)] + 2(k4-1) [f(x) + f(y)] +k2/4(k2-1) [f(2x) + f(2y)]where k is a real number ...  Read More

-23. Toeplitzness of weighted composition operators

Massoud Salehi Sarvestani

Volume 2, Issue 1 , April 2020, , Pages 1-8

http://dx.doi.org/10.30495/maca.2020.679850

Abstract
  For a bounded analytic map ψ on the unit disk D and analytic self-map  φ of D, a weighted composition operator Cψ,φ on the Hardy space H2=H2(D) is defined by  Cψ,φf= ψ·f°φ. In this paper, we study the asymptotically Toeplitzness ...  Read More

-22. Analytic differenceability of functions

Soodeh Mehboodi; Mohammad Hadi Hooshmand

Volume 3, Issue 1 , February 2021, , Pages 1-12

http://dx.doi.org/10.30495/maca.2021.680048

Abstract
  Analytic summability of functions was introduced by Hooshmand in 2016. He used Bernoulli numbers and polynomials Bn(z) to define analytic summability and related analytic summand functions. Since the Bernoulli and Euler polynomials have many similarities, so it motivated us to define differenceability ...  Read More

-21. Intuitionistic fuzzy stability of the heptic functional equation

Mohammad Shafii Mousavi

Volume 3, Issue 2 , June 2021, , Pages 1-14

http://dx.doi.org/10.30495/maca.2021.1926769.1006

Abstract
  In this article, by using a fixed point method, we establish the intuitionistic fuzzy version of Hyers-Ulam stability for a heptic functional equation that was introduced by Xu and Rassias. This way shows that the concept of stability is related to some fixed point of a suitable operator.  Read More

-20. On various types of compatible Jungck--Rhoades pairs of mappings in C*-algebra valued metric spaces

Parveen Kumar; Nicola Fabiano; Ljiljana Paunovic

Volume 3, Issue 3 , September 2021, , Pages 1-25

http://dx.doi.org/10.30495/maca.2021.1932335.1014

Abstract
  In this paper, among other things, we have established four different types of compatible mappings that work in the context of C*-algebra valued metric spaces. The obtained types of mappings generalize from previously known ones within ordinary metric spaces. We have shown by examples ...  Read More

-19. An existence result for a class of (p(x),q(x))-Laplacian system via sub-supersolution method

Saleh Shakeri

Volume 3, Issue 4 , December 2021, , Pages 1-8

http://dx.doi.org/10.30495/maca.2021.1937515.1024

Abstract
  This study concerns the existence of positive solution for the following nonlinear boundary value problem\begin{gather*}-\Delta_{p(x)} u= a(x)h(u) + f(v) \quad\text{in }\Omega\\-\Delta_{q(x)} v=b(x)k(v) + g(u) \quad\text{in }\Omega\\u=v= 0 \quad\text{on } \partial \Omega\end{gather*}where $p(x),q(x) ...  Read More

-18. Best simultaneous approximation in $L^{p}(S,X)$

Mohammad Valaei Anvar; Mohammad R Haddadi

Volume 4, Issue 1 , January 2022, , Pages 1-7

http://dx.doi.org/10.30495/maca.2021.1935786.1019

Abstract
  As a counterpart to the best approximation in normed linear spaces, the best simultaneous approximation was introduced. In this paper, we shall consider relation between simultaneous proximinality $W$ in $X$ and $L^p(S,W)$ in $L^p(S,X)$ for $1\leq p\leq\infty$. Also, we consider the relation between ...  Read More

-17. Some critical remarks of recent results on F-contractions in b-metric spaces

Mudasir Younis; Nicola Fabiano; Mirjana Pantovic; Stojan Radenovic

Volume 4, Issue 2 , April 2022, , Pages 1-10

http://dx.doi.org/10.30495/maca.2022.1948245.1043

Abstract
  In this paper, we analyze, generalize and correct some recent results on F-contractions within b-metric spaces. In all results, our only assumption is the strict growth of the function F: $\left( 0,+\infty \right) \rightarrow \left( -\infty ,+\infty \right) .$  Read More

-16. A simple method to solve nonlinear Volterra-Fredholm integro-differential equations

Mohsen Mohamadi; Amir Shahmari

Volume 2, Issue 1 , April 2020, , Pages 9-16

http://dx.doi.org/10.30495/maca.2020.679851

Abstract
  In this paper, a new simple direct method to solve nonlinear Fredholm-Volterra integral equations is presented. By using Block-pulse (BP) functions, their operational matrices and Taylor expansion a nonlinear Fredholm-Volterra integral equation converts to a nonlinear system. Some numerical examples ...  Read More

-14. Perturbed second-order state-dependent Moreau's sweeping process

Doria Affane; Mustapha Fateh Yarou

Volume 4, Issue 1 , January 2022, , Pages 9-23

http://dx.doi.org/10.30495/maca.2021.1938811.1029

Abstract
  In this paper, using a discretization approach, the existence of solutions for a class of second-order differential inclusions is stated in finite dimensional setting. The right hand side of the problem is governed by the so-called nonconvex state-dependent sweeping process and contains a general perturbation ...  Read More

-13. Automatic continuity of almost Jordan derivations on special Jordan Banach algebras

Ganesa Moorthy Chinnadurai; Siva Gurusamy

Volume 4, Issue 2 , April 2022, , Pages 11-16

http://dx.doi.org/10.30495/maca.2022.1946498.1040

Abstract
  The following is the question form of Kaplansky conjecture of 1958. Is every derivation on semisimple Banach algebra continuous? Kaplansky conjecture was proved by Johnson and Sinclair in 1968. The concept of almost Jordan derivations on Jordan Banach algebras is introduced in this article. Also, Kaplansky ...  Read More

-12. Generalized Ulam-Hyers stability of an alternate additive-quadratic-quartic functional equation in fuzzy Banach spaces

John Michael Rassias; Elumalai Sathya; Mohan Arunkumar

Volume 3, Issue 1 , February 2021, , Pages 13-31

http://dx.doi.org/10.30495/maca.2021.680135

Abstract
  In this paper, we obtain and establish the generalized Ulam-Hyers stability of an additive-quadratic-quartic functional equation in fuzzy Banach spaces.  Read More

-11. On a nonlinear abstract second-order integrodifferential equation part I

Mohammed Aijazuddin Hussain

Volume 3, Issue 4 , December 2021, , Pages 13-24

http://dx.doi.org/10.30495/maca.2021.1936023.1022

Abstract
  The object of this paper is to study the existence, uniqueness and continuation of the solutions of nonlinear second-order integrodifferential equations. In the theory of infinitesimal generator of $C_0$- semigroup in a Banach space, the fixed point theorems of Schauder and Banach are used to establish ...  Read More

-10. On character amenability of weighted convolution algebras on certain semigroups

Kobra Oustad

Volume 3, Issue 2 , June 2021, , Pages 15-26

http://dx.doi.org/10.30495/maca.2021.1928647.1007

Abstract
  In this work, we study the character amenability of weighted convolution algebras $\ell^{1} (S,\omega)$, where $ S $ is a semigroup of classes of inverse semigroups with a uniformly locally finite idempotent set, inverse semigroups with a finite number of idempotents, Clifford semigroups and Rees matrix ...  Read More

-9. The generalized Hyers–Ulam stability of derivations in non-Archimedean Banach algebras

Abolfazl Niazi Motlagh

Volume 2, Issue 1 , April 2020, , Pages 17-22

http://dx.doi.org/10.30495/maca.2020.679852

Abstract
  In this paper, the generalized Hyers-Ulam stability of the functional inequality||f(a)+f(b)+cf(d)+f(c)d||≤||kf((a+b+cd)/k)||,      |k|<|2|,in non-Archimedean Banach algebras is established.  Read More

-8. t-norms over fuzzy ideals (implicative, positive implicative) of BCK-algebras

Rasul Rasuli

Volume 4, Issue 2 , April 2022, , Pages 17-34

http://dx.doi.org/10.30495/maca.2021.1942817.1034

Abstract
  In this paper, we use the notion of t-norms to introduce fuzzy subalgebras, fuzzy ideals, fuzzy implicative ideals, fuzzy positive implicative ideals in BCK-algebras. Next, we clarify the links between them and investigate their properties. Finally, we consider them under intersection, cartesian product ...  Read More

-7. Locally finite inverse semigroups

Somaye Grailoo Tanha

Volume 2, Issue 1 , April 2020, , Pages 23-27

http://dx.doi.org/10.30495/maca.2020.679854

Abstract
  In this article, we study locally finite inverse semigroup S and characterize the structure of idempotents of S which are either a well-ordered countable chain or union of disjoint well-ordered countable chains. We also prove that whenS is a locally finite Clifford semigroup, S is ...  Read More

-6. Numerical solution of a coupled system of fractional order integro differential equations by an efficient numerical method based on the second kind Chebyshev polynomials

Mohammad Hossein Derakhshan

Volume 3, Issue 4 , December 2021, , Pages 25-40

http://dx.doi.org/10.30495/maca.2021.1938222.1025

Abstract
  In this paper, an efficient numerical method based on operational matrices of the second kind Chebyshev polynomials is used for the solution of a coupled system of fractional-order integrodifferential equations that the fractional derivative is given in Caputo's sense. The operational matrices of the ...  Read More

-5. On the zeros and critical points of a polynomial

Mohammad Ibrahim Mir; Irfan Ahmad Wani; Ishfaq Nazir

Volume 4, Issue 1 , January 2022, , Pages 25-28

http://dx.doi.org/10.30495/maca.2021.1938758.1028

Abstract
  Let $P(z)=a_0 + a_1z + \dots  + a_{n-1}z^{n-1}+z^n$ be a polynomial of degree $n.$  The Gauss-Lucas Theorem asserts that the zeros of the derivative $P^\prime (z)= a_1 + \dots  +(n-1) a_{n-1}z^{n-2}+nz^{n-1},$  lie in the convex hull of the zeros of   $P(z).$ Given a zero of ...  Read More

-4. Fixed point results for generalized contractions in S-metric spaces

Khalil Javed; Fahim Uddin; Faizan Adeel; Muhammad Arshad; Hossein Alaeidizaji; Vahid Parvaneh

Volume 3, Issue 2 , June 2021, , Pages 27-39

http://dx.doi.org/10.30495/maca.2021.1929557.1009

Abstract
  In this paper, we discuss the existence of a fixed point for a generalized contraction in S-metric spaces. We furnish some examples in support of our main results. Our results generalize and improve many well-known results in the existing literature.  Read More

-3. A new version of the Hahn Banach theorem in b-Banach spaces

Mohammad Reza Haddadi; Hossein Alaeidizaji; Vahid Parvaneh

Volume 3, Issue 3 , September 2021, , Pages 27-32

http://dx.doi.org/10.30495/maca.2021.1929965.1011

Abstract
  In this paper, we introduce the notion of b-Banach spaces and we present some examples. Also, we give an important extension of the Hahn-Banach theorem in a $b$-Banach space with an application.  Read More

-2. Certain dense subalgebras of continuous vector-valued operator algebras

Abbasali Shokri

Volume 2, Issue 1 , April 2020, , Pages 28-34

http://dx.doi.org/10.30495/maca.2020.679855

Abstract
  Let X be a compact metric space with at least two elements, B be a unital commutative Banach algebra over the scalar field F=R or C, and α in R with 0<α≤1. Suppose that C(X,B) be the continuous, A(X,B) be the analytic, and Lipα(X,B) be the α-Lipschitz B-valued ...  Read More

-1. Bicomplex valued bipolar metric spaces and fixed point theorems

Siva Gurusamy

Volume 4, Issue 1 , January 2022, , Pages 29-43

http://dx.doi.org/10.30495/maca.2021.1944542.1037

Abstract
  The concept of bicomplex valued bipolar metric space is introduced in this article, and some properties are derived. Also, some fixed point results of contravariant maps satisfying rational inequalities are proved for bicomplex valued bipolar metric spaces.  Read More

0. Some results on disjointness preserving Fredholm operators between certain Banach function algebras

Lida Mousavi; Sedigheh Hosseini

Volume 3, Issue 1 , February 2021, , Pages 32-39

http://dx.doi.org/10.30495/maca.2021.1924698.1002

Abstract
  For two algebras $\A$ and $\B$, a linear map $T : \A \lo \B$ is disjointness preserving if $x \cdot y = 0$ implies $Tx \cdot Ty = 0$ for all $x, y \in \A$ and is said Fredholm if dim(ker($T$)) i.e. the  nullity of $T$ and codim($T(E)$) i.e. the corank of $T$ are finite. We develop ...  Read More