Our paper is devoted to describing a new way of generalized convex contraction of type-2 in the framework of b-metric spaces and 2-metric spaces. First, the concept of a new generalized convex contraction on b-metric spaces and 2-metric spaces is introduced, and fixed point theorem is extended to these spaces. Some examples supporting our main results are also presented. Finally, we apply our main result to approximating the solution of the Fredholm integral equation.

In this paper, we consider several classes of mappings related to the class of $\alpha$-$ϝ$-contraction mappings by introducing a convexity condition and establish some fixed-point theorems for such mappings in complete metric spaces. The present result extends and generalizes the well-known results of $\alpha$-admissible and convex contraction mapping and many others in the existing literature. An illustrative example is also provided to exhibit the utility of our main results. Finally, we derive the existence and uniqueness of a solution to an integral equation to support our main result and give a numerical example to validate the application of our obtained results.

The idea of symmetry is a built-in feature of the metric function. In this paper, we investigate the existence and uniqueness of a fixed point of certain contraction via orthogonal triangular α-orbital admissible mapping in the context of orthogonal complete Branciari metric spaces endowed with a transitive binary relation. Our results generalize and extend some pioneering results in the literature. Furthermore, the existence criteria of the solutions to fractional integro-differential equations are established to demonstrate the applicability of our results.

In this paper, we introduce the concept of orthogonal convex structure contraction mapping and prove some fixed point theorems on orthogonal ♭-metric spaces. We adopt an example to highlight the utility of our main result. Finally, we apply our result to examine the existence and uniqueness of the solution for the spring-mass system via an integral equation with a numerical example.

In this article, we introduce a new concept of admissible contraction and prove fixed point theorems which generalize Banach contraction principle in a different way more than in the known results from the literature. The article includes an example which shows the validity of our results, and additionally we obtain a solution of integral equation by admissible contraction mapping in the setting of b-metric spaces.

In this paper, we prove a fixed point result in G-metric spaces satisfying generalized contractive condition with new auxiliary functions, which generalize the result of Bhardwaj and Kumar. The motivation of this paper is to observe the solution of an integral equation using the fixed point technique in G -metric space.