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In this paper, the authors prove some existence results for solutions for a new class of generalized bi-quasi-variational inequalities (GBQVI) for quasi-pseudo-monotone type I and strongly quasi-pseudo-monotone type I operators defined on non-compact sets in locally convex Hausdorff topological vector spaces. In obtaining these results on GBQVI for quasi-pseudo-monotone type I and strongly quasi-pseudo-monotone type I operators, we shall use Chowdhury and Tan’s generalized version of Ky Fan’s minimax inequality as the main tool.

Using the method of upper and lower solutions and its associated monotone iterative, we present an existence theorem for a nonlinear fractional differential equation with nonlinear boundary conditions.

In this paper, we obtain a successively iterative scheme of positive solution for the nonlinear third-order two-point boundary value problem u‴+q(u″)f(t,u)=0,u(0)=A,u(1)=B,u″(0)=C, where f is a Carathéodory function, f and q satisfy some additional monotone conditions. The iterative scheme starts off with zero function and is therefore useful for computation purpose. The main tool is monotone iterative technique on Banach space. Moreover, the iterative scheme is independent of the existence of lower and upper solutions.

This paper discusses anti-periodic boundary value problems of second order impulsive differential equations. By using the method of upper and lower solutions coupled with the monotone iterative technique, new existence results of coupled solutions and uniqueness of problems are obtained.

A new relaxed algorithmic procedure based on the notion of A-maximal relaxed monotonicity is developed, and then the convergence analysis in the context of solving a general class of nonlinear inclusion problems is examined. Furthermore, some results involving A-maximal relaxed monotone mappings in a Hilbert space setting are included.

A general design for the Eckstein–Bertsekas proximal point algorithm, using the notion of the A-maximal monotonicity, is developed. Convergence analysis for the generalized Eckstein–Bertsekas proximal point algorithm in the context of solving a class of nonlinear inclusion problems is explored. Some auxiliary results of interest involving A-maximal monotone mappings are also included. The obtained results generalize investigations on general maximal monotonicity and beyond.

This paper is concerned with the existence and uniqueness of monotone positive solutions for an elastic beam equation with nonlinear boundary conditions. The proof of our main results is based upon a new fixed point theorem of generalized concave operators.

This paper deals with the numerical analysis and simulation of nonlinear Black–Scholes equations modeling illiquid markets where the implementation of a dynamic hedging strategy affects the price process of the underlying asset. A monotone difference scheme ensuring nonnegative numerical solutions and avoiding unsuitable oscillations is proposed. Stability properties and consistency of the scheme are studied and numerical simulations involving changes in the market liquidity parameter are included.

In Bor (2011) [5], we proved a main theorem dealing with absolute Nörlund summability factors of infinite series. In the present paper, this result has been further generalized under weaker conditions by using δ-quasi-monotone sequences

In this paper, we are concerned with a two-competition model described by a reaction–diffusion system with nonlocal delays which account for the drift of individuals to their present position from their possible positions at previous times. By using the iterative technique recently developed in Wang et al. (2006) [14], the sufficient conditions are established for the existence of travelling wave solutions connecting the semi-trivial steady state to the coexistence steady state of the considered system. When the domain is bounded, we investigate the global attractivity of the coexistence steady state of the system under homogeneous Neumann boundary conditions as well. The approach used is the upper–lower solutions and monotone iteration technique.

This paper is concerned with the existence of extreme solutions of multi-point boundary value problem for a class of second-order functional differential equations. We introduce a new concept of lower and upper solutions. By using the method of upper and lower solutions and monotone iterative technique, we obtain the existence of extreme solutions.

In this paper, we propose some improvements on a new gradient-type method for solving large-scale unconstrained optimization problems, in which we use data from two previous steps to revise the current approximate Hessian. The new method which we considered, resembles to that of Barzilai and Borwein (BB) method. The innovation features of this approach consist in using approximation of the Hessian in diagonal matrix form based on the modified weak secant equation rather than the multiple of the identity matrix in the BB method. Using this approach, we can obtain a higher order accuracy of Hessian approximation when compares to other existing BB-type method. By incorporating a simple monotone strategy, the global convergence of the new method is achieved. Practical insights into the effectiveness of the proposed method are given by numerical comparison with the BB method and its variant.

In this note, we show some new inequalities of the Huygens type for circular functions, hyperbolic functions, and the reciprocals of circular and hyperbolic functions by using a monotone form of l’Hospital’s rule.