Common fixed point results under w-distance with applications to nonlinear integral equations and nonlinear fractional Differential Equations

In this article, we prove some new common fixed point results under the generalized contraction condition using w-distance and weak altering distance functions. Also, the validity of the results is demonstrated by an example along with numerical experiment for approximating the common fixed point. Later, as applications, the unique common solutions for the system of nonlinear Fredholm integral equations, nonlinear Volterra integral equations and nonlinear fractional differential equations of Caputo type are derived.

Fixed point results for weak contractions in partially ordered b-metric space

Objectives We explore the existence of a fixed point as well as the uniqueness of a mapping in an ordered b-metric space using a generalized $$({\check{\psi }}, \hat{\eta })$$ ( ψ ˇ , η ^ ) -weak contraction. In addition, some results are posed on a coincidence point and a coupled coincidence point of two mappings under the same contraction condition. These findings generalize and build on a few recent studies in the literature. At the end, we provided some examples to back up our findings. Result In partially ordered b-metric spaces, it is discussed how to obtain a fixed point and its uniqueness of a mapping, and also investigated the existence of a coincidence point and a coupled coincidence point for two mappings that satisfying generalized weak contraction conditions.

Set-valued Contractions in b-Metric Spaces with Application

In this article, we present a (α, F)-set-valued mapping in setting b-metric space by characterizing the weak contraction condition with the C function and the α-set-valued function of type S. There are examples and implementations accessible that illustrate the validity of our findings.

Changes in Spinal-Reflex Excitability during Static Stretch and/or Explosive Contraction

To examine individual or combined effects of static stretch and explosive contraction on quadriceps spinal-reflex excitability (the peak Hoffmann’s reflex normalized by the peak motor-response) and the latency times of the Hoffmann’s reflex and motor-response. Fourteen healthy young males randomly experienced four conditions (stretch, contraction, stretch + contraction, and control—no intervention). For the stretch condition, three sets of a 30 s hold using the modified Thomas test on each leg were performed. For the contraction condition, three trials of maximal countermovement vertical jump were performed. Quadriceps spinal-reflex excitability and the latent period of each value on the right leg were compared at pre- and post-condition. All measurement values across conditions were not changed at any time point (condition × time) in spinal-reflex excitability (F6,143 = 1.10, p = 0.36), Hoffmann’s reflex latency (F6,143 = 0.45, p = 0.84), motor-response latency (F6,143 = 0.37, p = 0.90), and vertical jump heights (F2,65 = 1.82, p = 0.17). A statistical trend was observed in the contraction condition that spinal-reflex excitability was increased by 42% (effect size: 0.63). Neither static stretch nor explosive contraction changed the quadriceps spinal-reflex excitability, latency of Hoffmann’s reflex, and motor-response. Since our stretch protocol did not affect jumping performance and our contraction protocol induced the post-activation potentiation effect, either protocol could be used as pre-exercise activity.

Common Fixed Points Technique for Existence of a Solution of Urysohn Type Integral Equations System in Complex Valued b-Metric Spaces

In this paper we give some common fixed point theorems for Ćirić type operators in complex valued b-metric spaces. Also, some corollaries under this contraction condition are obtained. Our results extend and generalize the results of Hammad et al. In the second part of the paper, in order to strengthen our main results, an illustrative example and some applications are given.

Fixed point theorems for a new generalization of contractive maps in incomplete metric spaces and its application in boundary value problems

In this paper, we obtain some fixed point theorems for multivalued mappings in incomplete metric spaces. Moreover, as motivated by the recent work of Olgun, Minak and Altun [M. Olgun, G. Minak and I. Altun, A new approach to Mizoguchi–Takahashi type fixed point theorems, J. Nonlinear Convex Anal. 17 2016, 3, 579–587], we improve these theorems with a new generalization contraction condition for multivalued mappings in incomplete metric spaces. This result is a significant generalization of some well-known results in the literature. Also, we provide some examples to show that our main theorems are a generalization of previous results. Finally, we give an application to a boundary value differential equation.

Perov multivalued contraction pair in rectangular cone metric spaces

Perov studied the Banach contraction principle in the framework of a generalized metric space and presented Perov contraction condition where the contractive constant is replaced by a matrix with nonnegative entries and spectral radius less than 1. Azam et al. presented the notion of rectangular cone metric space following the idea of Branciari, Huang and Zhang by replacing the triangular inequality in the cone metric space by rectangular inequality. Motivated by the work of Abbas and Vetro and Radenovi´c, the purpose of this paper is to introduce a new class of Perov type multivalued mappings and present a common fixed point result for such mappings on a complete rectangular cone metric space. Furthermore, an example is also presented to demonstrate the validity of our results. Our results extend, unify and generalize various comparable results in the existing literature.

(φ, ψ)-Contractıon Condition for Multivalued Mappings in Complete Modular Metric Spaces

In this paper we investigated (φ, ψ)-contractıon condition for multivalued type mappings in complete modular metric spaces. Our results are more general than metric versions of these type mappings.

Fixed point theorems for nonlinear contractive mappings in ordered b-metric space with auxiliary function

Objectives In this paper we present some fixed point theorems for self mappings satisfying generalized $$(\phi , \psi )$$ ( ϕ , ψ ) -weak contraction condition in partially ordered complete b-metric spaces. The results presented over here generalize and extend some existing results in the literature. Finally, we illustrate two examples to support our results. Result We obtained a unique fixed point of a self mapping satisfying certain contraction condition which is involving an auxiliary function. Also, the results are presented for the existence of a common fixed point and a coincidence point for generalized $$(\phi , \psi )$$ ( ϕ , ψ ) -weak contraction mappings in partially ordered complete b-metric space.