Ishikawa iterative process with errors for nonlinear equations of generalized monotone type in Banach spaces

The concept of the operators of generalized monotone type is introduced and iterative approximation methods for a fixed point of such operators by the Ishikawa and Mann iteration schemes {xn} and {yn} with errors is studied. Let X be a real Banach space and T : D ? X → 2^D be a multi‐valued operator of generalized monotone type with fixed points. A new general lemma on the convergence of real sequences is proved and used to show that {xn} converges strongly to a unique fixed point of T in D. This result is applied to the iterative approximation method for solutions of nonlinear equations with generalized strongly accretive operators. Our results generalize many of know results. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Variational Principles, Minimization Theorems, and Fixed-Point Theorems on Generalized Metric Spaces

In this paper, we prove a new minimization theorem by using the generalized Ekeland variational principle. We apply our minimization theorem to obtain some fixed-point theorems. Our results extend, improve, and unify many known results due to Kui, Ekeland, Takahashi, Caristi, iri, and others.     

Some common fixed point theorems for weakly compatible mappings

Jungck's [G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci. 9 (1986) 771-779] notion of compatible mappings is further extended and used to prove some common fixed point theorems for weakly compatible non-self mappings in complete convex metric spaces. We improve on the method of proof used by Rhoades [B.E. Rhoades, A fixed point theorem for non-self set-valued mappings, Int. J. Math. Math. Sci. 20 (1997) 9-12] and Ahmed and Rhoades [A. Ahmed, B.E. Rhoades, Some common fixed point theorems for compatible mappings, Indian J. Pure Appl. Math. 32 (2001) 1247-1254] and obtain generalization of some known results. In particular, a theorem by Rhoades [B.E. Rhoades, A fixed point theorem for non-self set-valued mappings, Int. J. Math. Math. Sci. 20 (1997) 9-12] is generalized and improved.     

General Strongly Nonlinear Quasivariational Inequalities with Relaxed Lipschitz and Relaxed Monotone Mappings

In this paper, we introduce and study a new class of general strongly nonlinear quasivariational inequalities and construct a general iterative algorithm by using the projection method. We establish the existence of a unique solution for general strongly nonlinear quasivariational inequalities involving relaxed Lipschitz, relaxed monotone, and strongly monotone mappings; we obtain the convergence and stability of the iterative sequences generated by the algorithm. Our results extend, improve, and unify many known results due to Bose, Noor, Siddiqi-Ansari, Verma, Yao, Zeng, and others.     

Hyperbolic heat conduction effects caused by temporally modulated laser pulses

In non-destructive testing (NDT), the intensity of laser pulses may be temporally modulated to improve the signal-to-noise ratio of ultrasonic signals. The purpose of this work is to determine the time scale on which hyperbolic heat conduction effects are significant in ultrasonic displacements and stresses for temporally modulated laser pulses, under the assumption that the heat wave speed equals the longitudinal wave speed. A one-dimensional model with a finite train of heat flux pulses is investigated. Using the Green and Lindsay model, it is found that the critical modulation frequency in steel, above which hyperbolic heat conduction effects will become signficant, is 2.26 GHz. A dimensionless factor is given to calculate critical modulation frequencies in other isotropic materials. The signal enhancement potential of temporal intensity modulation is apparent in the numerical results.     

On the steepest descent approximation method for the zeros of generalized accretive operators

In this paper we present certain characteristic conditions for the convergence of the generalized steepest descent approximation process to a zero of a generalized strongly accretive operator, defined on a uniformly smooth Banach space. Our study is based on an important result of Reich [S. Reich, An iterative procedure for constructing zeros of accretive sets in Banach spaces, Nonlinear Anal. 2 (1978) 85–92] and given results extend and improve some of the earlier results which include the steepest descent approximation method.     

Applications of Innovative Non-Thermal Pulsed Electric Field Technology in Developing Safer and Healthier Fruit Juices

The deactivation of degrading and pectinolytic enzymes is crucial in the fruit juice industry. In commercial fruit juice production, a variety of approaches are applied to inactivate degradative enzymes. One of the most extensively utilized traditional procedures for improving the general acceptability of juice is thermal heat treatment. The utilization of a non-thermal pulsed electric field (PEF) as a promising technology for retaining the fresh-like qualities of juice by efficiently inactivating enzymes and bacteria will be discussed in this review. Induced structural alteration provides for energy savings, reduced raw material waste, and the development of new products. PEF alters the α-helix conformation and changes the active site of enzymes. Furthermore, PEF-treated juices restore enzymatic activity during storage due to either partial enzyme inactivation or the presence of PEF-resistant isozymes. The increase in activity sites caused by structural changes causes the enzymes to be hyperactivated. PEF pretreatments or their combination with other nonthermal techniques improve enzyme activation. For endogenous enzyme inactivation, a clean-label hurdle technology based on PEF and mild temperature could be utilized instead of harsh heat treatments. Furthermore, by substituting or combining conventional pasteurization with PEF technology for improved preservation of both fruit and vegetable juices, PEF technology has enormous economic potential. PEF treatment has advantages not only in terms of product quality but also in terms of manufacturing. Extending the shelf life simplifies production planning and broadens the product range significantly. Supermarkets can be served from the warehouse by increasing storage stability. As storage stability improves, set-up and cleaning durations decrease, and flexibility increases, with only minor product adjustments required throughout the manufacturing process.     

On Properties of Solutions for a Class of Functional Equations Arising in Dynamic Programming

The existence, uniqueness, and iterative approximation of solutions for a class of functional equations arising in dynamic programming of multistage decision processes are discussed. Our results resolve in the affirmative an open problem posed in Ref. 1 and generalize important known results.     

Kinetics of Carbon Dioxide Reaction with Aqueous Mixture of Piperazine and 2‐Amino‐2‐ethyl‐1,3‐propanediol

Current researchers from environmental and industrial fields are focusing on advanced means of carbon dioxide (CO₂) capture to limit its consequences in process industries. They also intend to enhance the mitigation of environmental impart by CO₂ especially its greenhouse effect. In this study, the kinetics of CO₂ reaction with an aqueous blend of piperazine (PZ) and 2‐amino‐2‐ethyl‐1,3‐propanediol (AEPD) were investigated. It was found that blending of AEPD with a little percentage of PZ generated the observed rate constant, k_o, values that were more than twice the direct summation of the k_o values of the aqueous pure amines at the corresponding concentration and temperature. The kinetic study of the system was modeled using a termolecular mechanism. Blending 0.05 kmol/m³ of PZ with 0.5 kmol/m³ of AEPD gives an observed rate constant k_o value of 2397.9 s^?1 at 298 K. This result is comparable to rate constants of other amine mixtures. Thus, the aqueous blend of AEPD with PZ is an attractive solvent for CO₂ capture that has good advantages. The PZ that serves as the promoter in the reaction is needed in small fraction, whereas AEPD, which is a sterically hindered amine, increases CO₂ absorption capacity of the system. AEPD can be produced from renewable materials. © 2013 Wiley Periodicals, Inc. Int J Chem Kinet 45: 161–167, 2013