Let A be a bounded linear operator on a Banach space X. We investigate the conditions of existing rank-one operator B such that I+f(A)B is invertible for every analytic function f on sigma(A). Also we compare the invariant subspaces of f(A)B and B. This work is motivated by an operator method on the Banach space ell^2 for solving some PDEs which is extended to general operator space under some ...

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 the present paper, we refine notion of partial modular metric defined by Hosseinzadeh and Parvaneh to eliminate occurrence discrepancies in non-zero self-distance triangular inequality. support this, discuss non-trivial examples. Finally, prove a common fixed-point theorem for four self-mappings space an application our result; existence solution system Volterra integral equations is discuss...

we obtain two fixed point theorems for a kind of $varphi $-contractions incomplete fuzzy metric spaces, which are applied to easily deduceintuitionistic versions that improve and simplify the recent results of x.huang, c. zhu and x. wen.

in this paper,  the concept of fuzzy metric-like spaces is introduced which generalizes  the notion of fuzzy metric spaces given by george and veeramani cite{vee1}. some fixed point results for fuzzy contractive mappings on fuzzy metric-like spaces are derived. these results generalize several comparable results from the current literature. we also provide illustrative examples in support of ou...

We prove that the dimension $h^{1,1}_{\overline\partial}$ of space Dolbeault harmonic $(1,1)$-forms is not necessarily always equal to $b^-$ on a compact almost complex 4-manifold endowed with an Hermitian metric which locally conformally K\"ahler. Indeed, we provide examples non integrable, K\"ahler, structures 4-manifolds $h^{1,1}_{\overline\partial}=b^-+1$. This answers question by Holt.

In this paper we generalize the multivalued contraction theorem of S. B. Nadler [8]. As corollaries we obtain fixed point theorems for a multivalued function in complete dislocated metric spaces and complete partial metric space. 1991 Mathematics Subject Classification: 54H25, 47H10

In the present paper‎, ‎we show the existence of a coupled fixed point for a non-decreasing mapping in partially ordered complete metric space using a partial order induced by an appropriate function $phi$‎. ‎We also define the concept of weakly related mappings on an ordered space‎. ‎Moreover common coupled fixed points for two and three weakly related mappings are also proved in the same space‎.

There are a lot of fixed and common fixed point results in different types of spaces. For example, metric spaces, fuzzy metric spaces, and uniform spaces. One of the most interesting is partial metric space, which is defined by Matthews 1 . In partial metric spaces, the distance of a point in the self may not be zero. After the definition of partial metric space, Matthews proved the partial met...