In this paper, we are going to study the Hyers-Ulam-Rassias types of stability for nonlinear, nonhomogeneous Volterra integral equations with delay on finite intervals.

In this paper, we are going to study the Hyers-Ulam-Rassias types of stability for nonlinear, nonhomogeneous Volterra integral equations with delay on finite intervals.

Recently, Zhang and Song [Q. Zhang, Y. Song, Fixed point theory for generalized $varphi$-weak contractions, Appl. Math. Lett. 22(2009) 75-78] proved a common fixed point theorem for two maps satisfying generalized $varphi$-weak contractions. In this paper, we prove a common fixed point theorem for a family of compatible maps. In fact, a new generalization of Zhang and Song's theorem is given.

In this paper, we use the Riemann-Liouville fractional integrals to establish some new integral inequalities related to Chebyshev's functional in the case of two differentiable functions.

We investigate the long-term behavior of solutions of the difference equation$$x_{n+1}=x_{n}x_{n-3}-1, n=0,1, ldots $$where the initial conditions $x_{-3} ,, x_{-2} ,, x_{-1} ,, x_{0}$ are real numbers. In particular, we look at the periodicity and asymptotic periodicity of solutions, as well as the existence of unbounded solutions.

This paper deals with a new type of fixed point, i.e; "fixed point of order 2" which is introduced in a metric space and some results are achieved.

In this paper by using the idea of mean convergence, we introduce an iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the fixed points set of a nonspreading-type mappings in Hilbert space. A strong convergence theorem of the proposed iterative scheme is established under some control conditions. The main result of this paper extend the results obtained by Osilike and Isiogugu (Nonlinear Analysis 74 (2011) 1814-1822) and Kurokawa and Takahashi (Nonlinear Analysis 73 (2010) 1562-1568). We also give an example and numerical results arealso given.

In the paper [Y. Okuyama, On the absolute generalized Norlund summability of orthogonal series, Tamkang J. Math. Vol. 33, No. 2, (2002), 161-165] the author has found some sufficient conditions under which an orthogonal series is summable $|N,p,q|$ almost everywhere. These conditions are expressed in terms of coefficients of the series. It is the purpose of this paper to extend this result to double absolute summability $|N^{(2)},mathfrak{p},mathfrak{q}|_k$, $(1leq kleq 2)$.

A new class of nonlinear set-valued variational inclusions involving $(A,eta)$-monotone mappings in a Banach space setting is introduced and then based on the generalized resolvent operator technique associated with $(A,eta)$-monotonicity, the existence and approximation solvability of solutions using an iterative algorithm and fixed point theory is investigated.

In this article we consider relative iteration of entire functions and study comparative growth of the maximum term of iterated entire functions with that of the maximum term of the related functions.

In this paper we investigate the generalized Hyers-Ulam stability of the following Cauchy-Jensen type functional equation$$Q(frac{x+y}{2}+z)+Q(frac{x+z}{2}+y)+Q(frac{z+y}{2}+x) =2[Q(x)+Q(y)+Q(z)]$$ in non-Archimedean spaces.

In this paper, we introduce strongly $[ V_{2},lambda_{2},M,p]-$summable double sequence spaces via Orlicz function and examine some properties of the resulting these spaces. Also, we give natural relationship between these spaces and $S_{lambda_{2}}-$statistical convergence.

For an arbitrary entire function $f(z)$, let $M(f,R) = max_{|z|=R} |f(z)|$ and $m(f, r) =min_{|z|=r} |f(z)|$. If $P(z)$ is a polynomial of degree $n$ having no zeros in $|z| < k, k geq 1$, then for $0 leq r leqrholeq k$, it is proved by Aziz et al. that$$M(P',rho)leqfrac{n}{rho+k}{(frac{rho+k}{r+k})^n[1-frac{(k-rho)(n|a_0|-k|a_1|)n}{(rho^2+k^2)n|a_0|+2k^2rho |a_1|}(frac{rho-r}{k+r})(frac{k+1}{k+rho})^{n-1}]M(P,r)$$$$-[frac{(n|a_0|rho+k^2|a_1|)(r+k)}{(rho^2+k^2)n|a_0|+2k^2rho|a_1|}times[((frac{rho+k}{r+k})^n-1)-n(rho-r)]]m(P,k)}$$In this paper, we obtain a refinement of the above inequality. Moreover, we obtaina generalization of above inequality for $M(P', R)$, where $Rgeq k$.