https://www.macajournal.com/ Mathematical Analysis and its Contemporary Applications en daily 1 Mon, 01 Dec 2025 00:00:00 +0330 Mon, 01 Dec 2025 00:00:00 +0330 https://www.macajournal.com/article_731297.html This study presents a contraction referred to as fuzzy F-interpolative Berinde weak contraction, achieved by integrating two primary contractions, namely F-contraction and Berinde weak contraction, using a F-function within a fuzzy metric space. Utilizing this contraction, we have established a fixed point theorem applicable to self-mappings. To illustrate the implications of our results, we investigate the existence of solutions for nonlinear integral equations. An example has been devised to substantiate the established result. https://www.macajournal.com/article_725560.html We characterize norm-attaining functionals in locally convex spaces (LCS), with particular focus on three fundamental aspects: the weak-$^*$ (weak-star) topology in dual spaces, inductive limits (including LF-spaces and DF-spaces), and reflexivity conditions. Our main results establish that (1) norm-attainment in the weak-$^*$ dual coincides precisely with the canonical embedding $X \hookrightarrow X^{**}$; (2) strict inductive limits (such as $\mathcal{D}(\mathbb{R})$) permit non-attaining functionals, whereas Montel spaces ensure universal attainment; and (3) both barrelledness and reflexivity conditions recover norm-attainment through weak-$^*$ continuity. This work extends classical Banach space techniques to general LCS settings, revealing the crucial interplay between compactness properties and approximation methods in determining norm-attainment behavior. https://www.macajournal.com/article_731298.html In this article, we introduce weak contractive mappings and interpolative Kannan-type contraction mappings on a $2$-Banach space. In particular, we discuss the existence and uniqueness of a fixed point of such mappings in a $2$-Banach space. However, we define interpolative Reich-Rus-Ćirić type contraction mappings and interpolative Hardy-Rogers type contraction mappings, Kannan-Ćirić type contraction mappings and interpolative Kannan-Meir-Keeler type contractions on a $2$-Banach space. In particular, we prove the existence of a fixed point of such mappings in a $2$-Banach space. https://www.macajournal.com/article_731299.html This paper aims to obtain some new fixed point theorems in orbitally complete dislocated quasi-metric spaces for continuous self-mapping. This study opens new paths for research in dislocated quasi-metric spaces and enhances the ongoing progression of fixed point theory. https://www.macajournal.com/article_731503.html The orthogonality of derivations induced by operators is an area with various applications in light of ever-dynamic technological advances. There are different types of orthogonality, and interesting results have emerged in which operators satisfying given conditions are chosen to establish Range-Kernel orthogonality. However, most of the results have focused on one type of orthogonality called the Birkhoff orthogonality. We have also herein considered the Birkhoff concept of orthogonality. Researchers have repeatedly posed the following question: Could there be a possibility for studying other types of orthogonality with respect to the range and the kernel of derivations apart from the Birkhoff orthogonality? In this note, we establish orthogonality conditions for derivations when implemented by hyponormal operators underthe  Fuglede-Putnam property. https://www.macajournal.com/article_731614.html In this paper, we investigate two distinct classes of multivalent functions and establish sufficient conditions for a multivalent function to belong to these classes. The results presented here extend and unify existing criteria related to the starlikeness and convexity of multivalently analytic functions. By generalizing earlier findings, our work provides a broader framework for analyzing geometric properties and inclusion relationships within subclasses of analytic multivalent functions. https://www.macajournal.com/article_718542.html This remark addresses a typographical error in the paper [1]. The error is purely typographical and does not affect the validity of the results or conclusions presented. The corrected version is provided for clarity. https://www.macajournal.com/article_732573.html We present the concept of weak cyclic Bianchini ϕ-contraction mapping in this paper and demonstrate some findings regarding the best proximity points for these mappings in uniformly convex Banach spaces. This study builds upon the weak cyclic Bianchini contraction mapping and findings presented by Petric [17]. https://www.macajournal.com/article_733733.html In this article, we introduce interpolative Berinde weak type contraction mappings on a 2-Banach space. In particular, we discuss the existence of a fixed point of such a mapping in a 2-Banach space. However, we define a dual of interpolative Reich-Rus-Ćirić type contraction mappings and interpolative Hardy-Rogers type contraction mappings on 2-Banach spaces and complete metric spaces. In particular, we prove the existence of a fixed point of such mappings in 2-Banach spaces and complete metric spaces. On the other hand, we introduce interpolative Berinde-Ćirić type contraction mappings and interpolative Berinde-Meir-Keeler type contractions on a 2-Banach space. However, we prove the existence of a fixed point of such mappings in 2-Banach spaces. https://www.macajournal.com/article_733734.html In this paper, we investigate the existence and uniqueness of a fixed point for self-mappings satisfying integralcontractive conditions in complete S-multiplicative metric spaces. Also, we prove some common fixed points for pairs ofweakly compatible mappings satisfying integral-type contractive conditions in it. These results generalize and extend severalexisting fixed point theorems in the literature. An example is included to illustrate the main result. https://www.macajournal.com/article_736379.html In this paper, we introduce a new mapping called a proximal Gornicki type pair of mappings and prove the existence of common best proximity point theorems for such mappings without assuming continuity. We further prove the common best proximity point theorem for proximal enriched type pair of mappings and demonstrate the existence of the coupled common best proximity points theorem for such mappings in the literature. As applications of our main fixed point theorems, we present two Krasnoselskij projection-type algorithmsfor solving split feasibility problems and variational inequality problems.