1. 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 , Winter 2019, , Pages 1-43


  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

2. Toeplitzness of weighted composition operators

Massoud Salehi Sarvestani

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


  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

3. Analytic differenceability of functions

Soodeh Mehboodi; Mohammad Hadi Hooshmand

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


  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

4. Intuitionistic fuzzy stability of the heptic functional equation

Mohammad Shafii Mousavi

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


  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

5. 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 , Summer 2021, , Pages 1-25


  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

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

Saleh Shakeri

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


  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

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

Mohammad Valaei Anvar; Mohammad R Haddadi

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


  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

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

Mohsen Mohamadi; Amir Shahmari

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


  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

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

Doria Affane; Mustapha Fateh Yarou

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


  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

11. 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 , Winter 2021, , Pages 13-31


  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

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

Mohammed Aijazuddin Hussain

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


  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

13. On character amenability of weighted convolution algebras on certain semigroups

Kobra Oustad

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


  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

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

Abolfazl Niazi Motlagh

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


  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

15. Locally finite inverse semigroups

Somaye Grailoo Tanha

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


  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

16. 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 , Autumn 2021, , Pages 25-40


  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

17. On the zeros and critical points of a polynomial

Mohammad Ibrahim Mir; Irfan Ahmad Wani; Ishfaq Nazir

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


  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

18. 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 , Spring 2021, , Pages 27-39


  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

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

Mohammad Reza Haddadi; Hossein Alaeidizaji; Vahid Parvaneh

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


  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

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

Abbasali Shokri

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


  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

21. Bicomplex valued bipolar metric spaces and fixed point theorems

Siva Gurusamy

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


  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

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

Lida Mousavi; Sedigheh Hosseini

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


  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

23. On Palais method in b-metric like spaces

Nikola Mirkov; Zoran D. Mitrovic; Mudasir Younis; Stjan Radenovic

Volume 3, Issue 3 , Summer 2021, , Pages 33-38


  This paper aims to prove that the Lipschitz constant in the Banach contraction principle belongs to the whole interval [0, 1) for all the six classes of spaces viz. metric spaces, b-metric spaces, partial metric spaces, partial b-metric spaces, metric like space, and finally for more general spaces called ...  Read More

24. A new notion of affine sets

Paulraj Gnanachandra; Mohan Arunkumar

Volume 2, Issue 1 , Spring 2020, , Pages 35-42


  In this paper, we investigate the behaviour of e-convex sets and e-affine sets. Moreover, some notions like S(e,a,ρ,α) and e-affine cones are introduced and discussed. We complete with a role of above sets in linear idempotent maps.  Read More

25. Weakly principally quasi-Baer rings and generalized triangular matrix rings

Kamal Paykan

Volume 3, Issue 1 , Winter 2021, , Pages 39-45


  A ring $R$ is called weakly principally quasi-Baer or simply (weakly p.q.-Baer) if the right annihilator of a principal right ideal is right $s$-unital by right semicentral idempotents. In this paper, we characterize when a generalized triangular matrix ring is a weakly p.q.-Baer ...  Read More