Let P be cone Banach space E, A, K are two mappings in P, A accretive, K s k-set contraction, then fixed point index defined for mapping -A+K, some fixed point theorems are also deduced.

In this paper, we study the solution of the fractional nonlinear Ginzburg-Landau(FNGL) equation with weak initial data in the weighted Lebesgue spaces. The existence of a solution to this equation is proved by the contraction-mapping principle.

In this paper, we introduce generalized contraction mapping in fuzzy metric space. Some fixed point theorems for fuzzy metric space in the sense of George and Veeramani [2]. Mathematics Subject Classification: 47H10, 54A40.

In this paper, we prove some unique fixed point theorems for a fuzzy mapping T satisfying certain rational contraction condition in a partially ordered metric space. Our results generalize some existing result.

It is shown that a theorem of E. Rakotch for locally contractive mappings can be deduced from Banach's contraction mapping theorem, and a counterexample to an assertion of R. D. Holmes concerning local radial contractions is given. Let (X, d) be a metric space, k G (0, 1), and g a mapping of X into X. If for each x G X there exists a neighborhood A^(x) of x such that for each u, v G N(x), d(g(u...

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

Best approximation results provide an approximate solution to the fixed point equation $Tx=x$, when the non-self mapping $T$ has no fixed point. In particular, a well-known best approximation theorem, due to Fan cite{5}, asserts that if $K$ is a nonempty compact convex subset of a Hausdorff locally convex topological vector space $E$ and $T:Krightarrow E$ is a continuous mapping, then there exi...

In this work, the existence and uniqueness of solutions to a sequential fractional (Hybrid) differential equation with hybrid boundary conditions were investigated by generalization Dhage’s fixed point theorem Banach contraction mapping, respectively. addition, U-H technique is employed verify stability solution. This study ends two examples illustrating theoretical findings.