Akbar Azam

The aim of this paper is to present a novel stationary and nonstationary iterative approach for approximating common fixed points of a finite family of generalized nonexpansive mappings in uniformly convex Banach spaces. For the stationary scheme, both strong and weak convergence theorems are established under standard geometric conditions. Addressing an open problem, that is, “under what conditions nonstationary algorithm converge to a common fixed point of the generalized nonexpansive mapping,” thus we propose a nonstationary iterative method that dynamically adapts to varying parameters, and we derive sufficient conditions for its convergence. The asymptotic regularity and stability of the nonstationary method are rigorously analyzed. A comprehensive numerical example, supported by MATLAB simulations, demonstrates the practical convergence behavior of the proposed schemes and validates the theoretical findings. These results contribute to the growing body of fixed point theory and offer potential applications in areas such as signal processing, image reconstruction, and machine learning. MSC2020 Classification: 47H10, 47J26, 47H09, 46B06

A novel and generalized class of fractional differential inclusions has been investigated under a combination of nonlocal, non-separated, multipoint, and integral boundary conditions. Fractional derivatives have been employed to capture memory effects and enhance the modeling accuracy of real-world phenomena. Uncertainty has been addressed through the formulation of set-valued differential inclusions. The proposed boundary conditions have been designed to encompass a wide spectrum of both local and nonlocal types previously reported in the literature. The existence of solutions has been established via the Bohnenblust–Karlin fixed-point theorem. The applicability and effectiveness of the main results have been demonstrated through concrete examples.

A novel and generalized class of fractional differential inclusions has been investigated under a combination of nonlocal, non-separated, multipoint, and integral boundary conditions. Fractional derivatives have been employed to capture memory effects and enhance the modeling accuracy of realworld phenomena. Uncertainty has been addressed through the formulation of set-valued differential inclusions. The proposed boundary conditions have been designed to encompass a wide spectrum of both local and nonlocal types previously reported in the literature. The existence of solutions has been established via the Bohnenblust–Karlin fixed point theorem. The applicability and effectiveness of the main results have been demonstrated through concrete examples.

This paper presents a novel fixed point theorem for measurable selections arising from pairs of fuzzy set-valued operators defined on Polish spaces. By establishing conditions under which such selections exist, we provided a rigorous framework for analyzing the solvability of random multivalued operator equations in fuzzy environments. Our approach seamlessly integrated fuzziness and randomness, extending classical fixed point theory into a more realistic setting where uncertainty is both probabilistic and vague. To demonstrate the utility and applicability of our results, we constructed well-structured and insightful examples rooted in engineering-inspired scenarios. These examples not only validate the theoretical framework but also highlight its effectiveness in modeling complex systems affected by dual sources of uncertainty.

This paper introduced a novel concept of q‐rung orthopair fuzzy (q‐ROF) metric spaces, in connection with the idea of q‐ROF sets, which generalizes well‐known concepts of fuzzy metric spaces and intuitionistic fuzzy metric spaces. An elaborated example has been provided representing the increase in selection space due to the q‐ROF metric and limitations for the case of intuitionistic fuzzy metric space. We have presented the definitions of introduced concepts along with examples, so they are way more understandable for readers. Some basic topological results have been defined and proved for q‐ROF metric space. The concept of q‐ROF Menger boundedness is introduced, and its application in game theory is presented. Also we have presented the significance of introduced metric compared to existing versions of fuzzy metric in the consequent sections. Baire’s theorem and uniform limit theorem are also established in the perspective of q‐ROF metric spaces. An application of the obtained results in the field of game theory is also presented to draw the attention of investigators searching new fields of research.

This paper is dedicated to the advancement of fixed-point results for multi-valued asymptotically non-expansive maps regarding convergence criteria in complete uniformly convex hyperbolic metric spaces that are endowed with a graph. The famous fixed-point theorems of Goebel and Kirk, Khamsi and Khan, along with other recent results in the literature can be obtained as corollaries of these main results. A nice graph and an interesting example are also provided in support of the hypothesis of the main results.