Existence of best proximity points satisfying two constraint inequalities

In this paper, we prove the existence of best proximity point and coupled best proximity point on metric spaces with partial order for weak proximal contraction mappings such that these critical points satisfy some constraint inequalities.

A fuzzy fixed point problem for constraint inequalities

In this work, we prove a new fixed point theorem in the setting fuzzy metric spaces. The fuzzy metric space considered here is assumed to have two partial orders defined on it. We introduce a new approach to the existence of a fixed point of a function satisfying the two constraint inequalities. An example is included which illustrates new results of this paper. Moreover, an application of our result to the study of integral equations is provided.

Modeling of the limiting digging force of hydraulic excavator based on resistance characteristics

Based on the resistance characteristics, a model of theoretical digging force was proposed in this paper, taking the tangential force, the normal force, and the bending moment into account simultaneously. Utilizing the relation among the normal resistance, the resistance moment, and the tangential resistance in practical digging process, three independent unknown quantities are transformed into only one variable. Afterwards, according to different digging patterns and complete machine limiting conditions, this research derived the constraint inequalities of the limiting digging force (LDF) and established the calculation models for LDF. Then, based on the value distribution laws of the digging resistance coefficient and the resistance moment coefficient, the calculation process and corresponding method of LDF under a given digging posture were obtained. Taking the digging resistance obtained by testing for 35 t hydraulic excavator with backhoe attachment as the reference, this paper compared the calculation results of the theoretical digging force for complete machine with those of the LDF model proposed in this research. The comparative results indicate that the LDF is consistent with the fact that the theoretical digging force is larger than or at least equal to the actual digging resistance. So, the LDF can exactly show the real limiting digging ability of the excavator more accurately. In this way, it can provide basis for mechanism optimization, structural strength design, trajectory planning, and control automation of the excavator.

A fixed point problem with constraint inequalities via a contraction in incomplete metric spaces

In the present paper, firstly, we review the notion of the SO-complete metric spaces. This notion let us to consider some fixed point theorems for single-valued mappings in incomplete metric spaces. Secondly, as motivated by the recent work of H. Baghani et al.(A fixed point theorem for a new class of set-valued mappings in R-complete (not necessarily complete) metric spaces, Filomat, 31 (2017), 3875-3884), we obtain the results of Ansari et al. [J. Fixed Point Theory Appl. (2017), 1145-1163] with very much weaker conditions. Also, we provide some examples show that our main theorem is a generalization of previous results. Finally, we give an application to the boundary value system for our results.

Mathematical model for determination of the most advantageous conditions for formation of parts of aerospace engineering on the operations of the end milling

A mathematical model has been introduced for determining the most advantageous conditions for parts formation when end milling operations. This model consists of a linear objective function and linear inequality constraints and takes into account the kinetics of thermal processes in the cutting zone. The equation determines the processing time was used as the objective function and constraint inequalities are related with the functional parameters and the parameters of the milling process and determines the quality of the machining.

Analytical investigation on the minimum traffic delay at a two-phase intersection considering the dynamical evolution process of queues

This paper has studied the minimum traffic delay at a two-phase intersection, taking into account the dynamical evolution process of queues. The feature of delay function has been studied, which indicates that the minimum traffic delay must be achieved when at least one of the two constraint inequalities take the equal sign. We have derived the minimum delay as well as the corresponding traffic signal period, which shows that two situations are classified. Under certain circumstance, extra green time is needed for one phase while otherwise extra green time should be assigned to neither phase. Our work indicates that although the clearing policies were shown in many experiments to be optimal at isolated intersections, it is sometimes not the case.