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In this paper, we study the existence and uniqueness of mild solutions for second order initial value problems, with nonlocal conditions, by using the Banach fixed point theorem and the theory of strongly continuous cosine family.

In this paper, we investigate the existence, uniqueness and other properties of solutions of fractional semilinear evolution equations in Banach spaces. The results are obtained by using fractional calculus, the well-known Banach fixed point theorem coupled with Bielecki type norm and the integral inequality established by E. Hernandez.

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In this paper we investigate the existence and uniqueness for Volterra-Fredholm type integral equations in cone metric spaces. The result is obtained by using the some extensions of Banach's contraction principle in complete cone metric space.Mathematics Subject Classification: 45N05, 47G20, 34K05, 47H10.