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Throughout this manuscript, we investigate a new class of distance spaces, called €AB-distance in which a number of fixed point results can be achieved with the €AB-distance. Moreover, we offer a procedure for creating an extended b metric from a metric by employing €A, B-distance. Furthermore, this concept and the primary results are illustrated with examples. [ABSTRACT FROM AUTHOR]

Abstract In this manuscript, we use the concept of multidimensional fixed point in a generalized space, namely, C-distance space with some nonlinear contraction conditions, such as Jaggi- and Dass-Gupta-type contractions. We provide results with a Jaggi-type hybrid contraction for the mentioned space. Moreover, we use control functions to get the desired results. After each theorem, we compare our results with previous ones to show that they are generalized. We provide examples to support our results. An application is also performed to solve the system of integral equations.

Abstract In this paper, using the notion of w-distance in metric spaces, we introduce two types of nonlinear contractions, ( ι , ψ , φ , ϕ , p ) $(\iota ,\psi ,\varphi ,\phi ,p)$ and rational- ( ι , ψ , φ , ϕ , p ) $(\iota ,\psi , \varphi ,\phi ,p)$ contractions. Based on these contractions, we prove the existence and uniqueness of a φ-fixed point for the corresponding contraction. We also provide some examples to demonstrate the correctness and practicability of our results, along with a numerical experiment. Finally, we apply the obtained results to linear matrix equations and nonlinear Fredholm integral equations.

This article is devoted to enhancing a class of generalized Suzuki-type nonlinear contractions following Pant to a class of Suzuki–Ćirić-type nonlinear contractions via comparison functions via a locally ζ-transitive relation and implemented the same to ascertain certain fixed-point results. The outcomes presented herewith unify and generalize a few existing findings. An illustrative examples is offered to explain our findings. Our outcomes assist us in figuring out the unique solution to a boundary value problem.

In this paper, using the notion of w-distance in metric spaces, we introduce two types of nonlinear contractions, (ι , ψ , φ , ϕ , p) and rational- (ι , ψ , φ , ϕ , p) contractions. Based on these contractions, we prove the existence and uniqueness of a φ-fixed point for the corresponding contraction. We also provide some examples to demonstrate the correctness and practicability of our results, along with a numerical experiment. Finally, we apply the obtained results to linear matrix equations and nonlinear Fredholm integral equations. [ABSTRACT FROM AUTHOR]

In this paper, we establish some coincidence point theorems of nonlinear rational contractions in a complete partially ordered metric space. Some consequences of the results are presented in terms of integral contractions and few examples are illustrated to support the results. As an application, we proved the existence of a unique solution to an integral equation. [ABSTRACT FROM AUTHOR]

Abstract This work is for giving the probabilistic aspect to the known b-metric spaces (Czerwik in Atti Semin. Mat. Fis. Univ. Modena 46(2):263-276, 1998), which leads to studying the fixed point property for nonlinear contractions in this new class of spaces.

In this paper, we use the concepts of (A;B)-weakly increasing mappings and altering distance functions to establish new contractive conditions for the pair of mappings in the setting of G-metric spaces. Many Fixed and common Fixed point results in the setting of G{metric spaces are formulated. Note that our new contractive conditions can't be reduces to contractive conditions in standard metric spaces.

We give a probabilistic generalization of the theory of generalized metric spaces [2]. Then, we prove a fixed point theorem for a self-mapping of a probabilistic generalized metric space, satisfying the very general nonlinear contraction condition without the assumption that the space is Hausdorff.

In this paper, we introduce the notion of ultra distance function. Based on the notion of ultra distance function, we introduce the definitions of (k, ψ, L)-quasi contractions of type (I) and type (II) in the frame of quasi metric spaces. We employ our new definitions to construct and prove many fixed and common fixed point results in the frame of quasi metric spaces. Our results extend and improve many exciting results in the literatures. Also, we introduce some examples and some applications in order to support the usability of our work.

We give a probabilistic generalization of the theory of generalized metric spaces [2]. Then, we prove a fixed point theorem for a self-mapping of a probabilistic generalized metric space, satisfying the very general nonlinear contraction condition without the assumption that the space is Hausdorff. [ABSTRACT FROM AUTHOR]

In this paper, we derive and formulate many fixed point results of cyclic form under contractive conditions based on implicit relations in the setting of Ω-distance. Our results improve and generalize many existing results in the literature. Also, we introduce an example to show the validity of our main result.

We study boundary value problems of nonlinear fractional differential equations and inclusions of order $q in (m-1, m]$, $m ge 2$ with multi-strip boundary conditions. Multi-strip boundary conditions may be regarded as the generalization of multi-point boundary conditions. Our problem is new in the sense that we consider a nonlocal strip condition of the form: $$ x(1)=sum_{i=1}^{n-2}alpha_i int^{eta_i}_{zeta_i} x(s)ds, $$ which can be viewed as an extension of a multi-point nonlocal boundary condition: $$ x(1)=sum_{i=1}^{n-2}alpha_i x(eta_i). $$ In fact, the strip condition corresponds to a continuous distribution of the values of the unknown function on arbitrary finite segments $(zeta_i,eta_i)$ of the interval $[0,1]$ and the effect of these strips is accumulated at $x=1$. Such problems occur in the applied fields such as wave propagation and geophysics. Some new existence and uniqueness results are obtained by using a variety of fixed point theorems. Some illustrative examples are also discussed.

In 2006, Mustafa and Sims [18-19] introduced an improved version of the generalized metric space structure which they called G-metric spaces and in 2011; Berinde and Borcut [11] introduced the concept of triple fixed point. The intent of this paper is to establish some tripled fixed point theorems for mappings having mixed monotone property under nonlinear type contractions depended on another function in the framework of a G-metric space X enclosed with partial order. The presented results generalize, improve and extend corresponding results of H. Aydi et al. [13] (Tripled Fixed Point Results in Generalized Metric Spaces" Journal of Applied Mathematics Volume 2012, Article ID 314279, 10 pages, doi:10.1155/2012/314279). Moreover, some examples are provided to illustrate the usability of the obtained results. [ABSTRACT FROM AUTHOR]

Razani et al. studied the fixed points of nonlinear and asymptotic contractions in the modular space in 2007. In this paper, we generalize the kind of nonlinear contraction that is the result of Razani et al. (Abstr. Appl. Anal. 2007:40575, 2007) and prove the existence and uniqueness of fixed points for the generalized nonlinear contractions in modular spaces. [ABSTRACT FROM AUTHOR]

In this paper, we prove triple fixed point theorems in partially ordered metric spaces depended on another function. The presented results generalize the theorem of Berinde and Borcut [Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal. 74(15) (2011) 4889-4897]. Also, we state some examples showing that our results are effective. [ABSTRACT FROM AUTHOR]

We study boundary value problems of nonlinear fractional differential equations and inclusions of order q ∈ (m-1,m], m ≥ 2 with multi-strip boundary conditions. Multi-strip boundary conditions may be regarded as the generalization of multi-point boundary conditions. Our problem is new in the sense that we consider a nonlocal strip condition of the form: Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. which can be viewed as an extension of a multi-point nonlocal boundary condition: Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. In fact, the strip condition corresponds to a continuous distribution of the values of the unknown function on arbitrary finite segments (ςi, ηi) of the interval [0, 1] and the effect of these strips is accumulated at x = 1. Such problems occur in the applied fields such as wave propagation and geophysics. Some new existence and uniqueness results are obtained by using a variety of fixed point theorems. Some illustrative examples are also discussed. [ABSTRACT FROM AUTHOR]