Search

In this manuscript, we introduce the concept of complex-valued triple controlled metric spaces as an extension of rectangular metric type spaces. To validate our hypotheses and to show the usability of the Banach and Kannan fixed point results discussed herein, we present an application on Fredholm-type integral equations and an application on higher degree polynomial equations.

Taş, Nihal (Balikesir Author), In this paper, we deal with the geometric properties of non-unique fixed points for self-mappings of a metric space (resp. an S-metric space). The fixed-disc (resp. fixed-circle) problem has been investigated in this setting. To obtain new fixed-disc results, we modify some known fixed-point techniques. Illustrative examples are also given to show the validity of our main results., Scientific Research Project Fund of Balkesir University 2018/021 Prince Sultan University RG-DES-2017-01-17

In this manuscript, we useψ,ϕ-weak contraction to generalize coincidence point results which are established in the context of partially orderedb-metric spaces. The presented work explicitly generalized some recent results from the existing literature. Examples are also provided to show the authenticity of the established work.

In this paper, we introduce a new type of contraction to seek the existence of tripled best proximity point results. Here, using the new contraction and P-property, we generalize and extend results of W. Shatanawi and A. Pitea and prove the existence and uniqueness of some tripled best proximity point results. Examples are also given to support our results.

In this article, we discuss a new version of metric fixed point theory. The application of this newly introduced concept is to find some fixed point results where many well-known results in literature cannot be applied. We give some examples to illustrate the given concepts and obtained results.

In this paper, we give an affirmative answer to an open question posed recently by Mlaiki et al. As a consequence of our results, we get some known results in the literature. We also give an application of our results to the existence of a solution of nonlinear fractional differential equations.

This paper aims to introduce the notions of various types of Qc-contractions for which we establish some fixed circle and fixed disc theorems in the setting of metric spaces. Some illustrative examples are also provided to support our results. Moreover, we present some fixed circle and fixed disc results of integral type contractive self-mappings.

The aim of this article is to introduce the notion of a ϕ,&psi, metric space, which extends the metric space concept. In these spaces, the symmetry property is preserved. We present a natural topology &tau, ϕ,&psi, in such spaces and discuss their topological properties. We also establish the Banach contraction principle in the context of ϕ,&psi, metric spaces and we illustrate the significance of our main theorem by examples. Ultimately, as applications, the existence of a unique solution of Fredholm type integral equations in one and two dimensions is ensured and an example in support is given.

In this paper, we enlarge the class of C*-algebra valued partial metric spaces as well as the class of C*-algebra valued b-metric spaces by introducing the class of C*-algebra valued partial b-metric spaces and utilize the same to prove our fixed point results. We furnish an example to highlight the utility of our main result. Finally, we apply our result in order to examine the existence and uniqueness of a solution for the system of Fredholm integral equations.

In this paper, we introduce a new extension of the double controlled metric-type spaces, called double controlled metric-like spaces, by assuming that the “self-distance” may not be zero On the other hand, if the value of the metric is zero, then it has to be a “self-distance” (i.e., we replace $[\varsigma(g,h)=0 \Leftrightarrow g=h]$ [ ς ( g , h ) = 0 ⇔ g = h ] by $[\varsigma(g,h)=0 \Rightarrow g=h]$ [ ς ( g , h ) = 0 ⇒ g = h ] ). Using this new type of metric spaces, we generalize many results in the literature. We prove fixed point results along with examples illustrating our theorems. Also, we present double controlled metric-like spaces endowed with a graph along with an open question.

In this paper, we introduce a generalization of rectangular b-metric spaces, by changing the rectangular inequality as follows: Dζa,b≤ζa,b,u,vDζa,u+Dζu,v+Dζv,b, for all distinct a,b,u,v∈X. We prove some fixed point theorems, and we use our results to present a nice application in the last section of this paper.

In this work, we extend and complement some results in view of general and wider structures, such as b − metric spaces. By considering existing classes of Ζ − contractions and Ψ − simulating functions with a solid impact in database results of fixed point theory, we introduce a new general class of simulating functions, called as Ψ − s simulation functions, and also types of κ ψ − s − contractions in a more general framework. This approach covers, extends, and unifies several published works in the early and late literature.

We introduce some generalizations of contractions for multi-valued mappings and establish some fixed point theorems for multi-valued mappings in b -metric spaces. Our results generalize and extend several known results in b-metric spaces. Some examples are included which illustrate the cases when new results can be applied while old ones cannot.

Özgür, Nihal Yılmaz (Balikesir Author), In this paper, we introduce the concept of the rectangular M-metric spaces, along with its topology and we prove some fixed-point theorems under different contraction principles with various techniques. The obtained results generalize some classical fixed-point results such as the Banach's contraction principle, the Kannan's fixed-point theorem and the Chatterjea's fixed-point theorem. Also we give an application to the fixed-circle problem.

The notion of extended b-metric space plays an important role in the field of applied analysis to construct new theorems in the field of fixed point theory. In this paper, we construct and prove new theorems in the filed of fixed point theorems under some new contractions. Our results extend and modify many existing results in the literature. Also, we provide an example to show the validity of our results. Moreover, we apply our result to solve the existence and uniqueness of such equations.

Fixed point theory is a very important tool in mathematics and applied sciences. Latterly, many application examples have been presented for communication network and computer science fields. The proposed schema can be considered as a theoretical foundation for such a type of applications. In this paper, we introduce the notion of the $G_{m}$ -contraction to generalize and extend the notion of $G$ -contraction. We investigate the existence and uniqueness of the fixed point for such contractions in $M$ -metric space endowed with a graph. Our results extend and generalize various results in the existing literature, in particular the results of Jachymski. Some examples are included, which illustrate the results proved herein.

This paper aims to prove fixed point results for cyclic compatible contraction and Hardy–Rogers cyclic contraction in symmetric spaces. Our results generalize the results of Kumari and Panthi (2016) proved for cyclic compatible contraction and modified Hardy–Rogers cyclic contraction in the generating space of a b-quasi metric family and b-dislocated metric family. After that, as an application, we prove a fixed point result in symmetric pre-probabilistic metric spaces (PPM-spaces).

The aim of this paper is to generalize the F -contractive condition in the framework of &alpha, &minus, &nu, complete modular b-metric spaces. Some results in ordered modular b-metric spaces are also presented. Moreover, an illustrative example and some related applications are presented to support the obtained results.

Özgür, Nihal Yılmaz (Balikesir Author), In this paper, we prove new fixed-point theorems using the set of simulation functions on an S-metric space with some illustrative examples. Our results are stronger than some known fixed-point results. Furthermore, we give an application to the fixed-circle problem with respect to a simulation function., Prince Sultan University RG-DES-2017-01-17

The purpose of this paper is to introduce a new type of operators in graphical metric spaces and to prove some fixed point results for these operators. Several known results are generalized and extended in this new setting of graphical metric spaces. The results are illustrated and justified with examples.

In this paper, we specified a method that generalizes a number of fixed point results for single and multi-valued mappings in the structure of extended b-metric spaces. Our results extend several existing ones including the results of Aleksic et al. for single-valued mappings and the results of Nadler and Miculescu et al. for multi-valued mappings. Moreover, an example is given at the end to show the superiority of our results.

This article intends to initiate the study of Pompeiu–Hausdorff distance induced by an M-metric. The Nadler and Kannan type fixed point theorems for set-valued mappings are also established in the said spaces. Moreover, the discussion is supported with the aid of competent examples and a result on homotopy. This approach improves the current state of art in fixed point theory.

In this manuscript, we introduce the notions of various types of &Theta, c-contractions for which we establish some fixed circle and fixed disc theorems in the setting of metric spaces. Some illustrative examples are also provided to support our results. Moreover, we present some fixed circle and fixed disc results of integral type contractive self-mappings, which generalize many results of invariance and transformations in the literature.

In this paper we investigate some fixed-circle theorems using Ćirić’s technique (resp. Hardy-Rogers’ technique, Reich’s technique and Chatterjea’s technique) on a metric space. To do this, we define new types of F c -contractions such as Ćirić type, Hardy-Rogers type, Reich type and Chatterjea type. Two illustrative examples are presented to show the effectiveness of our results. Also, it is given an application of a Ćirić type F c -contraction to discontinuous self-mappings which have fixed circles.

Taş, Nihal (Balikesir Author), In this paper, we present new fixed-circle theorems for self-mappings on an S-metric space using some Wardowski type contractions, psi-contractive, and weakly psi-contractive self-mappings. The common property in all of the obtained theorems for Wardowski type contractions is that the self-mapping fixes both the circle and the disc with the center x(0) and the radius r., Prince Sultan University through research group Nonlinear Analysis Methods in Applied Mathematics (NAMAM) Group - RG-DES-2017-01-17

The study of asymmetric structures and their applications in mathematics is interesting. One of the types of asymmetric structures on a metric space has been initiated by Kada et al. (1996) and is known as a w-distance. That lack of symmetry attracts many researchers in fixed point theory. In this manuscript, we introduce a new type of contraction named generalized ( &alpha, &psi, M &Omega, ) -contractive mappings via w-distances, and then we prove some new related fixed point results, generalizing and improving the recent results of Lakzian et al. (2016) and others. At the end, we give some examples. To illustrate the usability of the new theory, we apply our obtained results to resolve a nonlinear Fredholm-integral-type equation.

We discuss recent fixed point results in b-metric spaces given by Pant and Panicker (2016). Our results are with shorter proofs. In addition, for &epsilon, &isin, ( 1 , 3 ] , our results are genuine generalizations of ones from Pant and Panicker.

In this manuscript, we introduce almost b-metric spaces and prove modifications of fixed point theorems for Reich and Hardy&ndash, Rogers type contractions. We present an approach generalizing some fixed point theorems to the case of almost b-metric spaces by reducing almost b-metrics to the corresponding b-metrics. Later, we show that this approach can not work for all kinds of contractions. To confirm this, we present a proof in which the contraction condition is such that it cannot be reduced to corresponding b-metrics.

Taş, Nihal (Balikesir Author), In this manuscript, we present some results related to fixed-discs of self-mappings in rectangular metric spaces. To do this, we give new techniques modifying some classical notions such as Banach contraction principle, -admissible mappings and Brianciari type contractions. We give necessary illustrative examples to show the validity of our obtained theoretical theorems. Our results are generalizations of some fixed-circle results existing in the literature., Balikesir University - 2018/021 Prince Sultan University through research group Nonlinear Analysis Methods in Applied Mathematics (NAMAM) - RG-DES-2017-01-17

In this paper, we ensure the existence and uniqueness of a best proximity point in rectangular metric spaces endowed with a graph structure.

Taş, Nihal (Balikesir Author) Özgür, Nihal Yılmaz (Balikesir Author), In this paper, we consider the fixed-circle problem on metric spaces and give new results on this problem. To do this, we present three types of F-C-Khan type contractions. Furthermore, we obtain some solutions to an open problem related to the common fixed-circle problem., Prince Sultan University for funding this work through research group Nonlinear Analysis Methods in Applied Mathematics (NAMAM) group number RG-DES-2017-01-17.

In this paper, we give an interesting extension of the partial S-metric space which was introduced [4] to the M_s-metric space. Also, we prove the existence and uniqueness of a fixed point for a self mapping on an Ms-metric space under different contraction principles.