/pdf/new-coupled-and-common-coupled-fixed-point-results-with-3cedjckars.pdf

New coupled and common coupled fixed point results with generalized c -distance on cone b -metric spaces

Abstract In this paper, we introduce the notions of T -Banach contraction, T Kannan contraction and T -Reich contraction in cone b-metric spaces under the concept of generalized c-distance. After that, we consider the mappings which satisfy the T -Reich contraction, T -Kannan contraction and T -Banach contraction and prove some fixed point theorems in such space with generalized c-distance. The obtained results generalize several well-known comparable results in literature.

/pdf/fixed-point-results-of-t-reich-contraction-t-kannan-4fgilahu8p.pdf

Fixed point results of T-Reich contraction, T-Kannan contraction and T-Banach contraction on cone b-metric spaces under generalized c-distance

In this work, we define the concept of a generalized c-distance in cone b-metric spaces over a Banach algebra and introduce some its properties. Then, we prove the existence and uniqueness of fixed points for mappings satisfying weak contractive conditions such as Han–Xu-type contraction and Cho-type contraction with respect to this distance. Our assertions are useful, since we remove the continuity condition of the mapping and the normality condition for the cone. Several examples are given to support the main results.

https://www.mdpi.com/2075-1680/9/1/31/pdf

Fixed Point Results under Generalized c-Distance in Cone b-Metric Spaces Over Banach Algebras

In this manuscript, we prove some fixed point theorems on C☆-algebra-valued partial b-metric spaces by using generalized contraction. We give support and suitable examples of our main results. Moreover, we present a generative application of the main results.

/pdf/fixed-point-results-in-c-algebra-valued-partial-b-metric-3rbcpei9.pdf

Fixed Point Results in C☆-Algebra-Valued Partial b-Metric Spaces with Related Application

In this study, we have new fixed point results for weak contraction mappings in complete and partially ordered b-metric spaces. Our findings expand and generalize the results of Jachymski and Mituku et al and many more results in the literature as well. To illustrate our work, we present an application on the existence and uniqueness of a nonlinear quadratic integral problem solution. Moreover, an open problem is presented to enable the scope for future research in this area. 

/pdf/fixed-point-theorems-of-almost-generalized-contractive-14977an7.pdf

Fixed Point Theorems of Almost Generalized Contractive Mappings in b-Metric Spaces and an Application to Integral Equation

In this paper, we consider the concept of cone b-metric spaces over Banach algebras and obtain some fixed point results for various definitions of contractive mappings. Moreover, we discuss about the property P and the property Q of fixed point problems. Our results are significant, since we omit the assumptions of normality of cones under which can be generalized and unified a number of recently announced results in the existing literature. In particular, we refer to the results of Huang et al. [H. Huang, G. Deng, S. Radenović, Some topological properties and fixed point results in cone metric spaces over Banach algebras, Positivity. (2018), in press].

/pdf/fixed-and-periodic-point-results-in-cone-b-metric-spaces-1sbqravch6.pdf

Ataollah Arabnia Firozjah

Papers

Fixed and periodic point results in cone b-metric spaces over Banach algebras; a survey

Fixed Point Results under Generalized c-Distance in Cone b-Metric Spaces Over Banach Algebras