This paper introduces some numerical algorithms for finding solutions of nonlinear problems like functional equations, split feasibility problems (SFPs) and variational inequality problems (VIPs) in the setting of Hilbert and Banach spaces. Our approach is based on the Thakur-Thakur-Postolache (TTP) iterative algorithm and the class of mean nonexpansive mappings. First we provide some convergence results (including weak and strong convergence) in the setting of Banach space. To support these results, we provide a numerical example and prove that our TTP algorithm in this case converges faster to fixed point compared to other iterative algorithms of the literature. After that, we consider two new TTP type projection iterative algorithms to solve SFPs and VIPs on the Hilbert space setting. Our result are new in analysis and suggest new type effective numerical algorithms for finding approximate solutions of some nonlinear problems.

Due to the lack of symmetry property for the quasi metrics, we have considered left and right versions of best proximity points of multivalued mappings of quasi metric spaces. Further we consider the problem of existence of semi (left and right) best proximity points of generalized multivalued contractions of quasi metric spaces via various versions of so called $p-$property. Some examples are given to explain the results.

This paper deals with the existence and uniqueness of the best proximity points of nonself-mappings in the context of non-Archimedean fuzzy metric spaces. The existence of different proximal quasi-contractive mappings allowed us to generalize some results concerning the existence and uniqueness of the best proximity points in the existing literature. Moreover, an application in computer science, particularly in the domain of words has been provided.

The eardrum is one of the most important organs in the body, and disorders such as infection or injury may affect the proper functioning of the eardrum and lead to hearing problems. In this paper, based on a real-world phenomena, we study some mathematical aspects of an abstract fractional $[\mathtt{p},\mathtt{q}]$-difference equation with initial conditions. Our initial value problem tries to model a vibrating eardrum by using the newly defined fractional Caputo-type $[\mathtt{p},\mathtt{q}]$-derivatives in two nonlinear single-valued and set-valued structures. We obtain a general form of the solutions in the framework of a $[\mathtt{p},\mathtt{q}]$-integral equation, and then we investigate the existence and uniqueness properties with the help of fixed points and the end-points of some special $\mathtt{\beta }$- $\mathtt{\alpha }$-contractions and compact mappings. Finally, we simulate this version of the vibrating eardrum model by giving two numerical examples to validate the established theorems.

In this study, changes in westerly waves and their connections to increased global warming under the influence of greenhouse gases were investigated via a Caputo fractional four-dimensional atmospheric system. The idea of the existence of chaotic behavior in the westerly wind's motion was depicted. It has been noted that westerlies are becoming stronger due to rising air temperatures. An analysis of the existence, uniqueness, boundedness, stability of equilibrium points, and conservative behavior of the solutions was conducted. To prove the existence of chaos in the modified model, the Lyapunov exponents, Poincaré map, and bifurcation were computed. A sliding mode controller to control the chaos in this novel fractional-order system was designed, and conditions for the global stability of the controlled system with and without external disturbances and uncertainties were derived. The finite-time interval for the system to reach the sliding surface was computed. The developed controller's performance was evaluated with respect to both commensurate and non-commensurate fractional derivatives. In each scenario, the impact of fractional orders was investigated. Numerical simulations were used to support theoretical statements about how the controller affects the system.

This paper presents and examines a newly improved linear technique for solving the equilibrium problem of a pseudomonotone operator and the fixed point problem of a nonexpansive mapping within a real Hilbert space framework. The technique relies two modified mildly inertial methods and the subgradient extragradient approach. In addition, it can be viewed as an advancement over the previously known inertial subgradient extragradient approach. Based on common assumptions, the algorithm's weak convergence has been established. Finally, in order to confirm the efficiency and benefit of the proposed algorithm, we present a few numerical experiments.