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In this study, firstly, the basic properties of the spectrum of the investigated problem were learned, sine and cosine type solutions were defined, their behaviors were examined and the properties of the solution of the given problem were learned with their help. Next, the characteristic equation of the studied problem was formed with the help of sine and cosine type solutions. Using the characteristic equation, the asymptotic behavior of the eigenvalues of the given problem and the ordering of the eigenvalues of the boundary value problems $L(\alpha _{j}),$ $j=1,$ $2$ when $\alpha_{1} $ $

In this paper, we construct the new integral representation of the Jost solution of Sturm-Liouville equation with impuls in the semi axis $[0,+\infty )$ and we give this type of relation, examine the properties of the Kernel function and their partial derivatives with $x$ and $\ t$, constructed integral representation and obtain the partial differential equation provided by this Kernel function. Finally, in the paper we prove uniqueness of the determination of the potential by the scattering data.

In this paper α-admissible contraction mappings on Branciari b-metric spaces are defined. Conditions for the existence and uniqueness of fixed points for these mappings are discussed and related theorems are proved. Various consequences of these theorems are given and specific examples are presented.

WOS: 000423281300008, In this paper, alpha-Meir-Keeler and generalized alpha-Meir-Keeler contractions on Branciari b-metric spaces are introduced. Existence and uniqueness of fixed points of such contractions are discussed and related theorems are proved. Various consequences of the main results are also presented.

WOS: 000393617200001, In this paper a class of general type alpha-admissible contraction mappings on quasi-b-metric-like spaces are defined. Existence and uniqueness of fixed points for this class of mappings is discussed and the results are applied to Ulam stability problems. Various consequences of the main results are obtained and illustrative examples are presented.

WOS: 000338938300001, A class of alpha-admissible contractions defined via altering distance functions is introduced. The existence and uniqueness conditions for fixed points of such maps on complete metric spaces are investigated and related fixed point theorems are presented. The results are reconsidered in the context of partially ordered metric spaces and applied to boundary value problems for differential equations with periodic boundary conditions.

WOS: 000338221900001, Existence and uniqueness of fixed points of a mapping defined on partially ordered G-metric spaces is discussed. The mapping satisfies contractive conditions based on certain classes of functions. The results are applied to the problems involving contractive conditions of integral type and to a particular type of initial value problems for the nonhomogeneous heat equation in one dimension. This work is a generalization of the results published recently in (Gordji et al. in Fixed Point Theory Appl. 2012:74, 2012, doi:10.1186/1687-1812-2012-74) to G-metric space.

WOS: 000327463000006, In this paper, we establish a solution to the following integral equation: u(t) = integral(T)(0) G(t, s)f(s, u(s)) ds for all t is an element of [0,T], (1) where T > 0, f : [0, T] x R -> R and G : [0, T] x [0, T] -> [0, infinity) are continuous functions. For this purpose, we also obtain some auxiliary fixed point results which generalize, improve and unify some fixed point theorems in the literature., Ministry of Science, Technology and Development, Republic of Serbia [174025], The authors thank the anonymous referees for their remarkable comments, suggestions and ideas that helped to improve this paper. The third author (V Rakocevic) is supported by Grant No. 174025 of the Ministry of Science, Technology and Development, Republic of Serbia.

WOS: 000350677900001, We introduce alpha-admissible Meir-Keller and generalized alpha-admissible Meir-Keller contractions on quasi-metric spaces and discuss the existence of fixed points of such contractions. We apply our results to G-metric spaces and express some fixed point theorems in G-metric spaces as consequences of the results in quasi-metric spaces.

WOS: 000316349000001, In this manuscript, we discuss the existence of a coupled coincidence point for mappings and , where F has the mixed g-monotone property, in the context of partially ordered metric spaces with an implicit relation. Our main theorem improves and extends various results in the literature. We also state some examples to illustrate our work. MSC: 47H10, 54H25, 46J10, 46J15.