Simulation functions and Meir–Keeler condensing operators with application to integral equations

We propose a new concept of condensing operators by using a notion of measure of non-compactness in the setting of Banach spaces and establish a new generalization of Darbo’s fixed point theorem. We also show the applicability of our results to integral equations. A concrete example will be presented to support the application part.

Near-Fixed Point Results via Ƶ-Contractions in Metric Interval and Normed Interval Spaces

Wu (2018) proved near-fixed point results in metric interval and normed interval spaces. In this paper, generalizing his work, we proved near-fixed point results in these interval spaces using α—admissibility and the concept of simulation functions. The results have been proved using Z-contractions.

A Brief Review on Validation for Heat Treatment Simulation

Heat treatment simulation has progressed to the stage where several commercial software are available. Validations of simulation functions using experimental results contributed to this realization. Organizing information on the validations may be effective for maintaining the functions and educating users about the nature of the phenomena. For this reason, the author here briefly reviews mainly his validation cases. Since experiments using specimens having relatively simple shapes can reveal the essence of complex phenomena, the results have been used in the validations. When the basic functions such as heat transfer, phase transformation, latent heat, and hardness prediction were comprehensively validated in the early stages of software development, the author used experimental results of the inverse hardening in quenched steel cylinders. After that, his validations of the software at the stage where adding stress and strain analysis functions, used effectively measurement data of length and diameter changes, and residual stress distributions in normally quenched steel cylinders. While, it was also worth to validate curving in long specimens cooled unevenly, which included a case of specimens with a similar cross-section to the Japanese sword. In addition, the author validated distortions and residual stresses in carburized and quenched, induction hardened, and also nitrided specimens.

A study of common fixed points that belong to zeros of a certain given function with applications

In this paper, we establish some point of φ-coincidence and common φ-fixed point results for two self-mappings defined on a metric space via extended CG-simulation functions. By giving an example we show that the obtained results are a proper extension of several well-known results in the existing literature. As applications of our results, we deduce some results in partial metric spaces besides proving an existence and uniqueness result on the solution of system of integral equations.

Data Dependence, Strict Fixed Point Results, and Well-Posedness of Multivalued Weakly Picard Operators

In this paper, we introduce the notion of s , r -contractive multivalued weakly Picard operators via simulation functions, named as Z s , r -contractions. We present some related fixed point theorems. We investigate data dependence and strict fixed point results. The well-posedness for such operators is also considered. Moreover, we generalize the results of Moţ and Petruşel. To show the usability of our results, we give some examples and an application to resolve a functional equation arising in dynamical systems.

Near-Coincidence Point Results in Norm Interval Spaces via Simulation Functions

Recently, Wu in 2018 established interesting results in the framework of interval spaces. He initiated the idea of near-fixed points and proved some related basic results in metric interval, norm interval, and hyperspaces. In 2015, Khojasteh et al. gave the concept of simulation functions and studied some fixed-point results in metric spaces. Motivated by this work, we give some near-coincidence point results in norm interval spaces using the concept given by Khojasteh et al. Examples are also provided for the validation of the results.

Existence theorem for integral inclusions by a fixed point theorem for multivalued implicit-type contractive mappings

In this article, we introduce fixed point theorems for multivalued mappings satisfying implicit-type contractive conditions based on a special form of simulation functions. We also provide an application of our result in integral inclusions. Our outcomes generalize/extend many existing fixed point results.

Fixed point theorems for generalized (beta-phi)-contractive pair of mappings using simulation functions

In this paper, our aim is to present a new class of generalized (beta-phi)-Z- contractive pair of mappings and we prove certain xed point theorems for a pair of mappings using this concept. Our results generalizes some xed point theorems in the literature. As an application some xed point theorems endowed with a partial order in metric spaces are also proved.