In this study, PPF dependent fixed point theorems are proved for a nonlinear operator, where the domain space $C[[a, b], E]$ is distinct from range space, $E$, which Strong Partial b-metric (SPbMS). We obtain existence and uniqueness of results defined mappings under SPbMS. Our extension in Examples provided support results.

In this paper, a new one-parameter class of fixed point iterative method is proposed to approximate the points contractive type mappings. The presence an arbitrary parameter in family increases its interval convergence. Further, we also propose two-step and three-step schemes. We discuss stability, strong convergence fastness methods. Furthermore, numerical experiments are performed check appli...

Abstract. A partial metric, also called a nonzero self-distance, is motivated by experience from computer science. Besides a lot of properties of partial metric analogous to those of metric, fixed point theorems in partial metric spaces have been studied recently. We establish several kinds of extended fixed point theorems in ordered partial metric spaces with higher dimension under generalized...

This paper is concerned with mixed monotone mappings in partially ordered cone metric spaces. We establish several fixed point theorems, which generalize and complement some known results. Especially, even in a partially ordered metric space, our main results are generalizations of the fixed point theorems due to Bhaskar and Lakshmikantham [T. Grana Bhaskar, V. Lakshmikantham, Fixed point theor...

In this paper, we prove several coupled common fixed point theorems for nonlinear mappings in a partially ordered probabilistic metric space. An example is presented to illustrate the main result of this paper.

*Correspondence: [email protected] Mathematics and Computer Science Department, Çankaya University, Eskişehir Yolu, Yenimahalle, Ankara, 06810, Turkey Abstract Recently, some authors have started to generalize fixed point theorems for contractive mappings in a class of generalized metric spaces in which the self-distance need not be zero. These spaces, partial metric spaces, were firs...